Question

8. Find the sum of n terms of an A.P. whose nth term is (2n + 1).
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Answer 1

Let, an Arithmetic progression of the form :

AP: a, a+d, a+2d, ..., a+(2n)d

So, the sum of all the terms is given by

$\sum _{k = 1} ^{2n + 1} (a + (k - 1)d)$

$S_{2n + 1} = \sum _{k = 1} ^{2n + 1}(a) + d\sum _{k = 1} ^{2n + 1}(k) - \sum _{k = 1} ^{2n + 1}(d)$

$S_{2n + 1} = {(2n + 1)}(a + nd)$